No. Early April intercourse would NOT lead to a pregnancy due in February. If she did in fact get pregnant from intercourse with you, she would be due at the end of December.
She most likely got pregnant mid May.
So this is not your baby.
No, the dates don't add up to you being the father. For a baby due in early February, she would have gotten pregnant in the second or early third week of May.
I assume this is something you merely casually wondered about once you heard she was pregnant? (She didn't call you and suggest you are the dad, right?)
I should mention just for your future poise in such situations, the price males pay for sex being much more freely available in today's culture than in your great-grandpa's wildest dreams is that sometimes a guy has to take a DNA test. If you were to get a request from her, handle it calmly. If it comes down to her wondering if it's you, that would mean she's pretty nervous and is trying to get all the definite information she can. So if she asks, tell her that the dates really don't add up, but if she's worried, go in and take a test. (With your head held high -- you were a month or a month and a half too early. But at least you won't be stonewalling like a jerk who thinks she was good enough to have sex with but not good enough to be kind to when she needed answers.) Testing voluntarily is always a decent thing to do if the situation arises. Go in person to a lab that the courts have approved to legally test for paternity (the family-law judge's clerk probably has a list). Never rely on an at-home drugstore test, they can be fudged. Keep in mind that it doesn't cost you anything (except the price of the test) to be gracious, and it is a lot less gracious to get a summons from a judge.
That all said, you aren't in the time range to be the dad. And, condoms are your best friend.